Since the function of the difference between the length of spring and non-compressed length is

Part A:
If the two lengths are equal then the difference will be 0, then equate f(theta) by 0


Subtract root 3 from both sides

Divide both sides by 2

Since the values of cos are negative in the 2nd and 3rd quadrant, then we will find the value of theta on them


n is any integers
Part B:
We will replace theta with 2 theta


n = 1 because the interval from [0, 2pi]
Then the value of theta in part 2 is half the value of theta in part 1
The function with 2theta is

Part C:
The other given equation is

We will equate the two functions to find the time

Subtract root 3 from both sides

Since

Then

Subtract 2cos theta from both sides

Take cos theta as a common factor

Equate each factor by 0 to find the value of theta


Then they have the same length at the time
